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Price-Fixing and Repeated Games

Price-Fixing and Repeated Games. Collusion and cartels. What is a cartel? attempt to enforce market discipline and reduce competition between a group of suppliers cartel members agree to coordinate their actions prices market shares exclusive territories

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Price-Fixing and Repeated Games

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  1. Price-Fixing and Repeated Games Chapter 14: Price-fixing and Repeated Games

  2. Collusion and cartels • What is a cartel? • attempt to enforce market discipline and reduce competition between a group of suppliers • cartel members agree to coordinate their actions • prices • market shares • exclusive territories • prevent excessive competition between the cartel members Chapter 14: Price-fixing and Repeated Games

  3. Collusion and cartels 2 • Cartels have always been with us; generally hidden • electrical conspiracy of the 1950s • garbage disposal in New York • Archer, Daniels, Midland • the vitamin conspiracy • But some are explicit and difficult to prevent • OPEC • De Beers • shipping conferences Chapter 14: Price-fixing and Repeated Games

  4. Recent events • Recent years have seen record-breaking fines being imposed on firms found guilty of being in cartels. For example • illegal conspiracies to fix prices and/or market shares • €479 million imposed on Thyssen for elevator conspiracy in 2007 • €396.5 million imposed on Siemens for switchgear cartel in 2007 • $300 million on Samsung for DRAM cartel in 2005 • Hoffman-LaRoche $500 million in 1999 • UCAR $110 million in 1998 • Archer-Daniels-Midland $100 million in 1996 Chapter 14: Price-fixing and Repeated Games

  5. Recent cartel violations 2 • Justice Department Cartel Fines grew steadily since 2002 Chapter 14: Price-fixing and Repeated Games

  6. Cartels • Two implications • cartels happen • generally illegal and yet firms deliberately break the law • Why? • pursuit of profits • But how can cartels be sustained? • cannot be enforced by legal means • so must resist the temptation to cheat on the cartel Chapter 14: Price-fixing and Repeated Games

  7. The incentive to collude • Is there a real incentive to belong to a cartel? • Is cheating so endemic that cartels fail? • If so, why worry about cartels? • Simple reason • without cartel laws legally enforceable contracts could be written De Beers is tacitly supported by the South African government • gives force to the threats that support this cartel • not to supply any company that deviates from the cartel • Investigate • incentive to form cartels • incentive to cheat • ability to detect cartels Chapter 14: Price-fixing and Repeated Games

  8. An example • Take a simple example • two identical Cournot firms making identical products • for each firm MC = $30 • market demand is P = 150 - Q • Q = q1 + q2 Price 150 Demand 30 MC Quantity 150 Chapter 14: Price-fixing and Repeated Games

  9. The incentive to collude Profit for firm 1 is: p1 = q1(P - c) = q1(150 - q1 - q2 - 30) = q1(120 - q1 - q2) Solve this for q1 To maximize, differentiate with respect to q1: p1/q1 = 120 - 2q1 - q2 = 0 q*1 = 60 - q2/2 This is the best response function for firm 1 The best response function for firm 2 is then: q*2 = 60 - q1/2 Chapter 14: Price-fixing and Repeated Games

  10. The incentive to collude 2 • Nash equilibrium quantities are q*1 = q*2 = 40 • Equilibrium price is P* = $70 • Profit to each firm is (70 – 30)x40 = $1,600. • Suppose that the firms cooperate to act as a monopoly • joint output of 60 shared equally at 30 units each • price of $90 • profit to each firm is $1,800 • But • there is an incentive to cheat • firm 1’s output of 30 is not a best response to firm 2’s output of 30 Chapter 14: Price-fixing and Repeated Games

  11. The incentive to cheat • Suppose that firm 2 is expected to produce 30 units • Then firm 1 will produce qd1 = 60 – q2/2 = 45 units • total output is 75 units • price is $75 • profit to firm 1 is $2,025 and to firm 2 is $1,350 • Of course firm 2 can make the same calculations! • We can summarize this in the pay-off matrix: Chapter 14: Price-fixing and Repeated Games

  12. The Incentive to cheat 2 Both firms have the incentive to cheat on their agreement This is the Nash equilibrium Firm 2 Cooperate (M) Deviate (D) Cooperate (M) (1800, 1800) (1250, 2250) Firm 1 (1600, 1600) Deviate (D) (2250, 1250) (1600, 1600) Chapter 14: Price-fixing and Repeated Games

  13. The incentive to cheat 3 • This is a prisoners’ dilemma game • mutual interest in cooperating • but cooperation is unsustainable • However, cartels to form • So there must be more to the story • consider a dynamic context • firms compete over time • potential to punish “bad” behavior and reward “good” • this is a repeated game framework Chapter 14: Price-fixing and Repeated Games

  14. Finitely repeated games • Suppose that interactions between the firms are repeated a finite number of times know to each firm in advance • opens potential for a reward/punishment strategy • “If you cooperate this period I will cooperate next period” • “If you deviate then I shall deviate.” • once again use the Nash equilibrium concept • Why might the game be finite? • non-renewable resource • proprietary knowledge protected by a finite patent • finitely-lived management team Chapter 14: Price-fixing and Repeated Games

  15. Firm 2 Cooperate (M) Deviate (D) (1800, 1800) (1250, 2250) Cooperate (M) Firm 1 Deviate (D) (2250, 1250) (1600, 1600) Finitely repeated games 2 • Original game but repeated twice • Consider the strategy for firm 1 • first play: cooperate • second play: cooperate if firm 2 cooperated in the first play, otherwise choose deviate Chapter 14: Price-fixing and Repeated Games

  16. Firm 2 Cooperate (M) Deviate (D) (1800, 1800) (1250, 2250) Cooperate (M) Firm 1 Deviate (D) (2250, 1250) (1600, 1600) Finitely repeated games 3 • This strategy is unsustainable • the promise is not credible • at end of period 1 firm 2 has a promise of cooperation from firm 1 in period 2 • but period 2 is the last period • dominant strategy for firm 1 in period 2 is to deviate Chapter 14: Price-fixing and Repeated Games

  17. Finitely repeated games 4 • Promise to cooperate in the second period is not credible • but suppose that there are more than two periods • with finite repetition for T periods the same problem arises • in period T any promise to cooperate is worthless • so deviate in period T • but then period T – 1 is effectively the “last” period • so deviate in T . . . and so on • Selten’s Theorem • “If a game with a unique equilibrium is played finitely many times its solution is that equilibrium played each and every time. Finitely repeated play of a unique Nash equilibrium is the equilibrium of the repeated game.” Chapter 14: Price-fixing and Repeated Games

  18. Finitely repeated games 5 • Selten’s theorem applies under two conditions • The one-period equilibrium for the game is unique • The game is repeated a finite number of times • Relaxing either of these two constraints leads to the possibility of a more cooperative equilibrium as an alternative to simple repetition of the one-shot equilibrium • Here, we focus on relaxing the second constraint and consider how matters change when the game is played over an infinite or indefinite horizon Chapter 14: Price-fixing and Repeated Games

  19. Repeated games with an infinite horizon • With finite games the cartel breaks down in the “last” period • assumes that we know when the game ends • what if we do not? • some probability in each period that the game will continue • indefinite end period • then the cartel might be able to continue indefinitely • in each period there is a likelihood that there will be a next period • so good behavior can be rewarded credibly • and bad behavior can be punished credibly Chapter 14: Price-fixing and Repeated Games

  20. Valuing indefinite profit streams • Suppose that in each period net profit is pt • Discount factor is R • Probability of continuation into the next period is r • Then the present value of profit is: • PV(pt) = p0 + Rrp1 + R2r2p2+…+ Rtrtpt+ … • valued at “probability adjusted discount factor” Rr • product of discount factor and probability of continuation Chapter 14: Price-fixing and Repeated Games

  21. Trigger strategies • Consider an indefinitely continued game • potentially infinite time horizon • Strategy to ensure compliance based on a trigger strategy • cooperate in the current period so long as all have cooperated in every previous period • deviate if there has ever been a deviation • Take our earlier example • period 1: produce cooperative output of 30 • period t: produce 30 so long as history of every previous period has been (30, 30); otherwise produce 40 in this and every subsequent period • Punishment triggered by deviation Chapter 14: Price-fixing and Repeated Games

  22. Cartel stability • Expected profit from sticking to the agreement is: • PVM= 1800 + 1800Rr + 1800R2r2 + … = 1800/(1 - Rr) • Expected profit from deviating from the agreement is • PVD = 2025 + 1600Rr + 1600R2r2 + … = 2025 + 1600Rr/(1 - Rr) • Sticking to the agreement is better if PVM > PVD • this requires 1800/(1 - Rr) > 2025 + 1600Rr/(1 - Rr) • or Rr > (2.025 – 1.8)/(2.025 – 1.6) = 0.529 • if r = 1 this requires that the discount rate is less than 89% • if r = 0.6 this requires that the discount rate is less than 14.4% Chapter 14: Price-fixing and Repeated Games

  23. Cartel stability 2 There is always a value of R < 1 for which this equation is satisfied • This is an example of a more general result • Suppose that in each period • profits to a firm from a collusive agreement are pC • profits from deviating from the agreement are pD • profits in the Nash equilibrium are pN • we expect that pD > pC > pN • Cheating on the cartel does not pay so long as: This is the short-run gain from cheating on the cartel This is the long-run loss from cheating on the cartel pD - pC Rr > pD - pN • The cartel is stable • if short-term gains from cheating are low relative to long-run losses • if cartel members value future profits (low discount rate) Chapter 14: Price-fixing and Repeated Games

  24. Trigger Strategy Issues • With infinitely repeated games • cooperation is sustainable through self-interest • But there are some caveats • examples assume speedy reaction to deviation • what if there is a delay in punishment? • trigger strategies will still work but the discount factor will have to be higher • harsh and unforgiving • particularly relevant if demand is uncertain • decline in sales might be a result of a “bad draw” rather than cheating on agreed quotas • so need agreed bounds on variation within which there is no retaliation • or agree that punishment lasts for a finite period of time Chapter 14: Price-fixing and Repeated Games

  25. The Folk theorem • Have assumed that cooperation is on the monopoly outcome • this need not be the case • there are many potential agreements that can be made and sustained – the Folk Theorem Suppose that an infinitely repeated game has a set of pay-offs that exceed the one-shot Nash equilibrium pay-offs for each and every firm. Then any set of feasible pay-offs that are preferred by all firms to the Nash equilibrium pay-offs can be supported as subgame perfect equilibria for the repeated game for some discount factor sufficiently close to unity. Chapter 14: Price-fixing and Repeated Games

  26. The Folk theorem 2 • Take example 1. The feasible pay-offs describe the following possibilities p2 The Folk Theorem states that any point in this triangle is a potential equilibrium for the repeated game $1800 to each firm may not be sustainable but something less will be $3600 Collusion on monopoly gives each firm $1800 $2000 If the firms collude perfectly they share $3,600 If the firms compete they each earn $1600 $1800 $1600 p1 $1800 $1500 $1600 $2000 $3600 Chapter 14: Price-fixing and Repeated Games

  27. Balancing temptation • A collusive agreement must balance the temptation to cheat • In some cases the monopoly outcome may not be sustainable • too strong a temptation to cheat • But the folk theorem indicates that collusion is still feasible • there will be a collusive agreement: • that is better than competition • that is not subject to the temptation to cheat Chapter 14: Price-fixing and Repeated Games

  28. Antitrust Policy & Collusion • Ideally, antitrust policy can act to deter cartel formation • To do this, authorities must investigate/monitor industries and, when wrongdoing is found, prosecute and punish • However, theauthorities can not monitor every market. • So, for any cartel, there is only a probability that it will be investigated and discovered • Assume: Probability of investigation is a; Probability of successful prosecution given investigation is s Punishment if successfully prosecuted if fine, F Chapter 14: Price-fixing and Repeated Games

  29. Antitrust Policy & Collusion 2 • Combining our investigation and prosecution assumptions with our earlier model of collusion yields the following expected profit for each cartel member as M – asF + 1 –  VC= 1 – (1 – as) • In our earlier analysis a = s = F = 0. It is clear in examining the above equation that an increase in either the probability of investigation a, or in the probability of successful prosecution s, or in the punishment | fine F, will decrease expected cartel profits and so make cartel formation less likely • MORAL: Policy against cartels works by deterring their formation in the first place and not perhaps so much as by breaking them up once they happen Chapter 14: Price-fixing and Repeated Games

  30. Antitrust Policy & Collusion 3 • Which tool the authorities should rely most on— a, s, or F—depends on a number of factors. • Even a small fine may do the trick if the probability of detection and prosecution asis high enough. • However, monitoring, investigating, and prosecuting are expensive whereas fines are relatively costless to impose. This suggests that optimal policy will cut back on expensive detection efforts and balance this by imposing heavy fines for those cartels that are detected. Chapter 14: Price-fixing and Repeated Games

  31. Empirical Application: Estimating the Effects of Price Fixing • An important question for policy-makers and scholars alike is precisely what is the effect of cartels when they do happen. Basically, how different is the market price set by a cartel from the price that would have prevailed in the absence of the cartel? • Both theory and empirical technique can be used to determine this “but for” price, the price that would have prevailed “but for” the cartel. Chapter 14: Price-fixing and Repeated Games

  32. Empirical Application: Estimating the Effects of Price Fixing 2 • Kwoka (1997) provides an interesting econometric study that yields information on the “but for” price in the case of a real estate cartel in the Washington, D.C. area • Because of foreclosure as well as for other reasons, real estate properties are often sold at auctions. In the DC area during the 1980’s, realtors established a bidding cartel that agreed to submit artificially low prices with one cartel member chosen to win the auction the price at a low bid P. Chapter 14: Price-fixing and Repeated Games

  33. Empirical Application: Estimating the Effects of Price Fixing 3 • After the public auction, the cartel members would meet and hold a private “Knockout” auction. Denote the winning bid in this round as K. • Suppose that there were N cartel members. After compensation of the original buyer, each of the N – 1 losers in the knockout round would then receive a payment of S= (K – P)/(N– 1). Chapter 14: Price-fixing and Repeated Games

  34. Empirical Application: Estimating the Effects of Price Fixing 4 • If the true market value of the real estate is V, the winner of the knockout round gets V – K. In equilibrium, the losers and winners will only be satisfied with their respective outcomes if S = V – K. So, we can write: N(K – P) K – P NK + (N – 1)P – NP V = K + S = K + = = P + N - 1 N – 1 N – 1 • Kwoka then assumes that cartel members set the public winning bid P in constant proportion to the true value V such that V = mP . Substitution and solving for K then yields: (N – 1) K = P + (m – 1) P N Chapter 14: Price-fixing and Repeated Games

  35. Empirical Application: Estimating the Effects of Price Fixing 5 • Kwoka (1997) knows K, P, and N. He uses ordinary regression analysis to estimate the slope term m – 1 and hence, m. Using different assumptions about the auction and the compensation of knockout round losers. He estimates m is between 1.48 and 1.88. • Recall that P = V/m. These estimates then imply that the bid-rigging cartels led to public bids that were somewhere between 54% and 67% of the true value. • In other words, the bid-rigging cartel depressed public auction prices by somewhere on the order of 33% to 46%. Chapter 14: Price-fixing and Repeated Games

  36. Summary • Infinite/indefinite repetition raises possibility of price-fixing • stable cartels sustained by credible threats • so long as discount rate is not too high • and probability of continuation is not too low • Public Policy concern about cartels is justified • Deterrence is at least as important as breaking up existing cartels • Deterrence rises with • probability of detection and • punishment if caught • Cartels happen as evidenced by numerous recent cases and price effects can be large, say as much as 33 percent Chapter 14: Price-fixing and Repeated Games

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